Abstract.Widespread flooding, such as the events in the winter of 2013/2014 in the UK and early summer 2013 in Central Europe, demonstrate clearly how important it is to understand the characteristics of floods in which multiple locations experience extreme river flows. Recent developments in multivariate statistical modelling help to place such events in a probabilistic framework. It is now possible to perform joint probability analysis of events defined in terms of physical variables at hundreds of locations simultaneously, over multiple variables (including river flows, rainfall and sea levels), combined with analysis of temporal dependence to capture the evolution of events over a large domain. Critical constraints on such data-driven methods are the problems of missing data, especially where records over a network are not all concurrent, the joint analysis of several different physical variables, and the choice of suitable time scales when combining information from those variables. T his paper presents new developments of a high-dimensional conditional probability model for extreme river flow events conditioned on flow and r ainfall observations. T hese are: a new computationally efficient parametric approach to account for missing data in the joint analysis of ex tremes over a large hydrometric network; a robust approach for the spatial interpolation of extreme events throughout a large river network,; generation of realistic estimates of extremes at ungauged locations; and, exploiting rainfall information rationally within the statistical model to help improve efficiency. T hese methodological advances will be illustrated with data from the UK river network and recent events to show how they contribute to a flexible and effective framework for flood risk assessment, with applications in the insurance sector and for national-scale emergency planning.